1 Methods

1.1 Ground-truth data

Table 1.1: Table 1.2: Properties of test tracks used to compare position estimations and accuracies for maisC (C1-4) and maisD (D1-4). N points is the number of recorded GPS positions (summarized in 2-second intervals) and N tags the number of used transmitters.
track ID date duration (h) length (km) N points N tags
C1 2023-10-05 0.73 3.33 1259 3
C2 2023-10-09 2.99 10.59 5371 4
C3 2023-10-10 3.00 11.74 5401 4
Ctest 2023-10-13 1.05 5.07 1744 4
D1 2023-09-07 4.32 7.30 3406 3
D2 2023-09-16 1.81 3.30 3219 3
D3 2023-09-28 2.36 6.63 4250 3
Dtest 2023-09-13 1.47 3.96 2646 3

1.2 Station cover

Exemplified calculation of detection probability (left) and station cover (summed up detection probabilities across all stations, right) for directional antennas in maisC. Copyright map data: OpenStreetMap contributors

Figure 1.1: Exemplified calculation of detection probability (left) and station cover (summed up detection probabilities across all stations, right) for directional antennas in maisC. Copyright map data: OpenStreetMap contributors

2 Results

2.1 Estimated positions

maisC 0.5m

Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 0.5 m above ground in maisC. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

Figure 2.1: Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 0.5 m above ground in maisC. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

maisC 1m

Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 1 m above ground in maisC. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

Figure 2.2: Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 1 m above ground in maisC. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

maisC 1.5m

Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 1.5 m above ground in maisC. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

Figure 2.3: Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 1.5 m above ground in maisC. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

maisC 2m

Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 2 m above ground in maisC. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

Figure 2.4: Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 2 m above ground in maisC. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

maisC all meth.

Overview whether positions in maisC could be estimated by all methods ('yes', orange) or not ('no', grey) per testtrack (columns) and test transmitter (rows, the label depicts the transmitter's height above ground in m). Note that transmitter 2 was not used for test track C1.

Figure 2.5: Overview whether positions in maisC could be estimated by all methods (‘yes’, orange) or not (‘no’, grey) per testtrack (columns) and test transmitter (rows, the label depicts the transmitter’s height above ground in m). Note that transmitter 2 was not used for test track C1.

maisD 0.5m

Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 0.5 m above ground in maisD. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

Figure 2.6: Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 0.5 m above ground in maisD. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

maisD 1m

Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 1 m above ground in maisD. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

Figure 2.7: Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 1 m above ground in maisD. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

maisD 1.5m

Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 1.5 m above ground in maisD. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

Figure 2.8: Position errors (PE) of estimated positions per testtrack (columns) and method (rows) for a test transmitter at 1.5 m above ground in maisD. Ground-truth positions are displayed and colored by PE. Positions that could not be estimated are colored in gray. Note the log10 scaling of the PE color scale.

maisD all meth.

Overview whether positions in mais D could be estimated by all methods ('yes', orange) or not ('no', grey) per testtrack (columns) and test transmitter (rows, the label depicts the transmitter's height above ground in m).

Figure 2.9: Overview whether positions in mais D could be estimated by all methods (‘yes’, orange) or not (‘no’, grey) per testtrack (columns) and test transmitter (rows, the label depicts the transmitter’s height above ground in m).

2.2 Correlations between predictors

direct ab - maisC

Correlations between predictors (Ac = number of receiving antennas, Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB), Weight = summed up normalized signals), including correlation coefficients (upper panels) and histograms (diagonal panels) for directional antenna beams in maisC.

Figure 2.10: Correlations between predictors (Ac = number of receiving antennas, Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB), Weight = summed up normalized signals), including correlation coefficients (upper panels) and histograms (diagonal panels) for directional antenna beams in maisC.

direct ab - maisD

Correlations between predictors (Ac = number of receiving antennas, Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB), Weight = summed up normalized signals), including correlation coefficients (upper panels) and histograms (diagonal panels) for directional antenna beams in maisD.

Figure 2.11: Correlations between predictors (Ac = number of receiving antennas, Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB), Weight = summed up normalized signals), including correlation coefficients (upper panels) and histograms (diagonal panels) for directional antenna beams in maisD.

direct in - maisC

Correlations between predictors (Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB)), including correlation coefficients (upper panels) and histograms (diagonal panels) for directional intersection in maisC.

Figure 2.12: Correlations between predictors (Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB)), including correlation coefficients (upper panels) and histograms (diagonal panels) for directional intersection in maisC.

direct in - maisD

Correlations between predictors (Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB)), including correlation coefficients (upper panels) and histograms (diagonal panels) for directional intersection in maisD.

Figure 2.13: Correlations between predictors (Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB)), including correlation coefficients (upper panels) and histograms (diagonal panels) for directional intersection in maisD.

omni ab - maisC

Correlations between predictors (Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB), Weight = summed up normalized signals), including correlation coefficients (upper panels) and histograms (diagonal panels) for omnidirectional antenna beams in maisC.

Figure 2.14: Correlations between predictors (Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB), Weight = summed up normalized signals), including correlation coefficients (upper panels) and histograms (diagonal panels) for omnidirectional antenna beams in maisC.

omni ml - maisC

Correlations between predictors (Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB)), including correlation coefficients (upper panels) and histograms (diagonal panels) for omnidirectional multilateration in maisC.

Figure 2.15: Correlations between predictors (Sc = number of receiving stations, cover = station cover (proxy for detection probability), maxSig = maximum received signal (dB)), including correlation coefficients (upper panels) and histograms (diagonal panels) for omnidirectional multilateration in maisC.

2.3 Position error and accuracy

PA

Predicted mean PE (pPE, based on 4000 simulated datasets) from the global model, namely the median pPE (triangle) including 50 % (thick bar) and 95 % CI (thin bar), as well as the distribution (polygon, only center and bottom panels) for all present combinations of Ac-Sc per site and method. For predictions, maxSig, (weight) and cover were set to their respective raw data mean per Ac-Sc combination.

Figure 2.16: Predicted mean PE (pPE, based on 4000 simulated datasets) from the global model, namely the median pPE (triangle) including 50 % (thick bar) and 95 % CI (thin bar), as well as the distribution (polygon, only center and bottom panels) for all present combinations of Ac-Sc per site and method. For predictions, maxSig, (weight) and cover were set to their respective raw data mean per Ac-Sc combination.

PA50

Predicted median PE (pPE50, based on 4000 simulated datasets) from the global model, namely the median estimated 50% quantile of PE (triangle) including 50 % (thick bar) and 95 % CI (thin bar), as well as the distribution (polygon, only center and bottom panels) for all present combinations of Ac-Sc per site and method. For predictions, maxSig, (weight) and cover were set to their respective raw data mean per Ac-Sc combination.

Figure 2.17: Predicted median PE (pPE50, based on 4000 simulated datasets) from the global model, namely the median estimated 50% quantile of PE (triangle) including 50 % (thick bar) and 95 % CI (thin bar), as well as the distribution (polygon, only center and bottom panels) for all present combinations of Ac-Sc per site and method. For predictions, maxSig, (weight) and cover were set to their respective raw data mean per Ac-Sc combination.

PA65

Predicted 65% quantile of PE (pPE65, based on 4000 simulated datasets) from the global model, namely the median estimated 65% quantile of PE (triangle) including 50 % (thick bar) and 95 % CI (thin bar), as well as the distribution (polygon, only center and bottom panels) for all present combinations of Ac-Sc per site and method. For predictions, maxSig, (weight) and cover were set to their respective raw data mean per Ac-Sc combination.

Figure 2.18: Predicted 65% quantile of PE (pPE65, based on 4000 simulated datasets) from the global model, namely the median estimated 65% quantile of PE (triangle) including 50 % (thick bar) and 95 % CI (thin bar), as well as the distribution (polygon, only center and bottom panels) for all present combinations of Ac-Sc per site and method. For predictions, maxSig, (weight) and cover were set to their respective raw data mean per Ac-Sc combination.